Gear differentials generally include compound planetary gear sets interconnecting a pair of drive shafts for opposite directions of rotation with respect to a differential housing. So-called "side" or "end" gears, which form sun gear members of the compound planetary gear sets, are rotatively coupled to inner ends of the two drive shafts. The sun gears are interconnected for the opposite directions of rotation by so-called "element" or "spider" gears, which form the planet gear members of the sets. The planet gears are mounted for rotation about axes that may be variously offset and inclined with respect to a common axis of the sun gears and drive shafts.
In fact, the relative positions of the sun and planet gear axes in large part determine the kind of gearing that make up the planetary gear sets. For example, parallel axes are used for mounting spur or helical gears. Orthagonal axes are used for mounting either bevel or worm gears, depending upon the presence of any offset between the axes. Bevel gears are used when the sun and planet gear axes intersect, whereas worm gears are used when the gear axes do not intersect.
Although much less common, crossed-axis helical gears have also been used to form the compound planetary gear sets of gear differentials. Crossed-axis helical gears are mounted on axes that are offset from one another and inclined to one another at an acute angle.
Two examples of this type of differential are found in U.S. Pat. No. 1297954 (WILLIAMS). The side (sun) gears in both examples are interconnected by element (planet) gears mounted in pairs about parallel axes that are mutually inclined to a common axis of the side gears. One of the two examples includes side gears with teeth oriented to the same hand (sign) of helix angle; and in the other example, the two side gears have teeth with opposite hand helix angles. The absolute magnitudes of the opposite hand helix angles of the side gears are also different.
However, since the element gear members of each pair mesh with each other on parallel axes, the helix angles of the meshing element gears must be equal in absolute magnitude but opposite in hand (i.e., sum to zero degrees). If the absolute magnitude of the element gear helix angles is less than the shaft angle between the side and element gears, then the side gears are of the same hand, differing from one another in magnitude by twice the absolute magnitude of the element gear helix angles. In contrast, if the shaft angle is less than the absolute magnitude of the element gear helix angles, then the side gears are of opposite hand, differing from one another in absolute magnitude by twice the shaft angle.
These limitations pose special problems with torque distributions between the output shafts of crossed-axis planetary gear differentials. If the side gears are of the same hand helix angle or if the helix angles of the two side gears differ significantly in absolute magnitude, then, in response to the application of drive torque to the differential housing, the side gears generate a considerable thrust force against one end of the housing. The thrust force produces between one side gear and the housing frictional torque that encourages the transmission of torque from the differential housing to one of the drive shafts in response to one direction of relative rotation between the drive shafts (i.e., differentiation) and resists the transmission of housing torque to the same drive shaft in response to the opposite direction of differentiation. As a result, torque is distributed to the respective drive shafts in uneven proportions between the opposite directions of differentiation.
Both of the crossed-axis planetary gear examples of Williams have side gears with helix angles that are expected to generate considerable thrust against one end of the differential housing. The element gears in one of Williams' examples are spur gears. Accordingly, both side gears have helix angles equal to the shaft angle at which the element gear axes are inclined to the common axis of the side gears. The other of Williams' examples has element gears with opposite hand helix angles of an equal absolute magnitude that is greater than the shaft angle. Although the side gears are also of opposite hand, they differ in absolute magnitude by twice the shaft angle. Thus, both of Williams' examples have side gear helix angles that are expected to generate thrust forces that produce uneven torque distributions between the drive shafts compared during opposite directions of differentiation.
Crossed-axis helical gears are also known to have very limited load carrying capabilities. Both members of crossed-axis helical gear sets are conventional parallel axis gears (i.e., helical or spur gears) having cylindrical pitch surfaces. However, since the gear members are mounted on axes that are inclined to each other, the pitch surfaces of the gears have only point contact with each other. This greatly increases contact stresses on the gear teeth of crossed-axis helical gears in comparison with teeth of helical and spur gears mounted on parallel axis, which have line contact or more teeth in contact.